F-theta lens

Abstract: An f lens for scanning light emanating from a deflecting point comprising a first lens having a positive refracting power and a second lens having a negative refracting power, the first and second lenses being cemented together with the first lens positioned on the entrance pupil side and satisfying the following formulae (10) to (12), wherein n d1 and n d2 respectively represent the refractive indices for the sodium d-line of the first and second lenses, ν d1 and ν d2 respectively represent the Abbe's numbers for the sodium d-line of the first and second lenses, and  1 represents the power of the first lens standardized on the basis of the power of the whole system, said f lens being used in a position where the distance between the deflecting point and the entrance pupil side surface of the first lens standardized on the basis of the focal length of the whole system is in the range of 0.1 to 0.4 inclusive.

Description: This invention relates to a scanning optical system. Description of the Prior Art Recently there has been put into wide use various instruments such as a laser beam printer in which a laser beam scanning optical system is used. In such an optical system, an f lens is used to cause a laser beam, which is deflected by a rotary polygonal mirror or the like, to scan the surface of a medium at a constant speed. The f lens is a lens which satisfies a condition that Y=f wherein  represents the incident angle of the laser beam to the lens, f represents the focal length of the lens and Y represents the height of the image formed. Conventionally the f lens is designed on the assumption that a monochromatic or single wavelength laser beam is used and accordingly the color aberration causes no problem and correction of the color aberration has been unnecessary heretofore. However, for instance, in a laser recording system in which color images are recorded on silver salt film by use of a plurality of laser beams having different wavelengths, e.g., red, green and blue laser beams, the problem of color aberration must be taken into account. As is well known in the art, the color aberration includes the axial color aberration and the lateral color aberration. The axial color aberration shifts the position of the image in the direction of the optical axis depending on the wavelength and practically does not cause a serious problem since the focal depth of the laser beam is sufficiently large. However, the lateral color aberration causes the position of the image to shift in the direction perpendicular to the optical axis depending on the wavelength, and accordingly, the beam is shifted in the scanning direction by different distance depending on the wavelength, which makes it impossible to precisely superimpose the spots of the respective colors one on another and adversely affects the quality of images. Though this problem may be overcome by operating the laser beams of the respective colors in different timings, this approach requires complicated control and is not suitable for high-speed scanning. In Japanese Patent Publication No. 61(1986)-51289, there is disclosed a technique for correcting lateral color aberration. However this technique can correct lateral color aberration only by a wavelength of 20nm and is originally developed to correct color aberration due to fluctuation in wavelength of a semiconductor laser. Accordingly it cannot be applied to a multiple wavelength scanning optical system for color image recording. An f lens disclosed in Japanese Unexamined Patent Publication No. 62(1987)-262812 can correct the lateral color aberration for two or more laser beams with a high accuracy under predetermined conditions. However the f lens comprises four elements in three lens groups. When the number of lens elements is large, the manufacturing cost increases, and at the same time, errors in processing the lens elements and assembly of the same can accumulate. Further in order to satisfy the disclosed conditions, the material for the lens elements must be selected within a narrow range. US-A-3,973,833 discloses a scanning optical system including a deflecting surface and a f lens for receiving scanning light emanating from said deflecting surface, said f lens comprising a first lens having a positive refracting power and a second lens having a negative refracting power, with the first lens positioned on the entrance pupil side, wherein the following formulae (1) to (3) are satisfied n d1 < n d2 0.4 ≤ ν d2 /ν d1 ≤ 0.8 1.5 ≤  1 ≤ 4.7 wherein n d1 and n d2 respectively represent the refractive indices for the sodium d-line of the first and second lenses, ν d1 and ν d2 respectively represent the Abbe's numbers for the sodium d-line of the first and second lenses, and  1 represents the power of the first lens standardized on the basis of the power of the whole system. Specifically, the lens shown in figure 2 of said US'833 has the following parameters: n d1 = 1.648; n d2 = 1.762, µ d2 /µ d1 = 0,78 and  1 = 2.1. SUMMARY OF THE INVENTION In view of the foregoing observations and description, the primary object of the present invention is to provide an f lens which can correct the color aberration with a high accuracy over a wide wavelength range, and consists of a small number of lens elements to permit reduction of the size of the optical system, the manufacturing cost and the error in assembly. This is achieved by an optical scanning system defined in the patent claim. In accordance with the present invention, there is provided a scanning optical system having a f lens for scanning light emanating from a deflecting point comprising a first lens having a positive refracting power and second lens having a negative refracting power, the first and second lenses being cemented together with the first lens positioned on the entrance pupil side (deflecting point side) and satisfying the following formulae (1) to (3), n d1 <n d2 0.4≦ν d2 /ν d1 ≦0.8 1.5≦ 1 ≦4.7 wherein n d1 and n d2 respectively represent the refractive indices for the sodium d-line of the first and second lenses, ν d1 and ν d2 respectively represent the Abbe's numbers for the sodium d-line of the first and second lenses, and  1 represents the power of the first lens standardized on the basis of the power of the whole system, said f lens being used in a position where the distance between the deflecting point and the entrance pupil side surface of the first lens standardized on the basis of the focal length of the whole system is in the range of 0.1 to 0.4 inclusive (either of these values being standardized on the basis of the focal length of the whole system). The lens elements of the f lens in accordance with the present invention need not be limited to spherical lenses but may be aspheric lenses. The f lens in accordance with the present invention comprises only two lens elements in a single lens group and simple in structure. Further when the formulae (1) to (3) are satisfied and the f lens being used in a position where the distance between the deflecting point and the entrance pupil side surface of the first lens standardized on the basis of the focal length of the whole system is in the range of 0.1 to 0.4 inclusive, the color aberration can be corrected over a wide wavelength range. The formula (1) limits the relation between the refractive indices for the sodium d-line of the first and second lenses. When the refractive index of the first lens is not smaller than that of the second lens, the color aberration becomes too large in the positive direction and at the same time, the amount of curvature of field in the three-dimensional meridional image surface becomes too large in the negative direction, whereby it becomes difficult to correct both the color aberration and the curvature of field. The formula (2) limits the relation between the Abbe's numbers of the first and second lenses forming a cemented lens group. The ratio of the Abbe's numbers governs the amount of color aberration generated at the interface between the first and second lenses. When the ratio of the Abbe's numbers of the first and second lenses is larger than 0.8, the color aberration generated at the interface in the negative direction becomes small and the color aberration in the positive direction increases as a whole, which results in under correction. On the other hand, when the ratio of the Abbe's numbers of the first and second lenses is smaller than 0.4, the color aberration generated at the interface in the negative direction becomes large and the color aberration in the negative direction increases as a whole, which results in over correction. The formula (3) relates to the Petzval sum and limits the amount of curvature of field. That is, when the power of the first lens standardized on the basis of the power of the whole system is larger than the upper limit 4.7, the f characteristic becomes too large in the positive direction to correct and at the same time, the amount of curvature of field in the three-dimensional meridional image surface becomes too large in the negative direction to correct. On the other hand, when the power of the first lens is smaller than the lower limit 1.5, the amount of curvature of field in the three-dimensional meridional image surface becomes too large in the positive direction to correct. Further, since the f characteristic depends on the distance from the entrance pupil as described above, the distance between the deflecting point (the intersection of the deflecting surface and the optical axis) and the surface of the first lens must be in a predetermined range. When the distance between the deflecting point and the surface of the first lens standardized on the basis of the focal length of the whole system is smaller than the lower limit 0.1, the f characteristic becomes too large in the positive direction to correct, and when it is larger than the upper limit 0.4, the f characteristic becomes too large in the negative direction to correct and at the same time, the size of the second lens group increases, which adds to the manufacturing cost of the f lens. Further when the distance is smaller than the lower limit, the amount of curvature of field in the three-dimensional meridional image surface becomes too large in the negative direction to correct and when the distance is larger than the upper limit, the amount of curvature of field in the three-dimensional meridional image surface becomes too large in the positive direction to correct. Figure 1A is a view showing the arrangement of the lens elements in an f lens of a first embodiment in accordance with the present invention, Figure 1B is a graph showing the lateral color aberration of the f lens shown in Figure 1A for three wavelengths W1, W2 and W3, Figure 1C is a graph showing the astigmatic field curves (curvature of field) of the f lens shown in Figure 1A for the three wavelengths W1, W2 and W3, Figure 1D is a graph showing the linearity (f characteristic) of the f lens shown in Figure 1A for the three wavelengths W1, W2 and W3, Figure 2A is a view showing the arrangement of the lens elements in an f lens of a second embodiment in accordance with the present invention, Figure 2B is a graph showing the lateral color aberration of the f lens shown in Figure 2A for three wavelengths W1, W2 and W3, Figure 2C is a graph showing the astigmatic field curves (curvature of field) of the f lens shown in Figure 2A for the three wavelengths W1, W2 and W3, Figure 2D is a graph showing the linearity (f characteristic) of the f lens shown in Figure 2A for the three wavelengths W1, W2 and W3, Figure 3A is a view showing the arrangement of the lens elements in an f lens of a third embodiment in accordance with the present invention, Figure 3B is a graph showing the lateral color aberration of the f lens shown in Figure 3A for three wavelengths W1, W2 and W3, Figure 3C is a graph showing the astigmatic field curves (curvature of field) of the f lens shown in Figure 3A for the three wavelengths W1, W2 and W3, Figure 3D is a graph showing the linearity (f characteristic) of the f lens shown in Figure 3A for the three wavelengths W1, W2 and W3, Figure 4A is a view showing the arrangement of the lens elements in an f lens of a fourth embodiment in accordance with the present invention, Figure 4B is a graph showing the lateral color aberration of the f lens shown in Figure 4A for three wavelengths W1, W2 and W3, Figure 4C is a graph showing the astigmatic field curves (curvature of field) of the f lens shown in Figure 4A for the three wavelengths W1, W2 and W3, Figure 4D is a graph showing the linearity (f characteristic) of the f lens shown in Figure 4A for the three wavelengths W1, W2 and W3, Figure 5A is a view showing the arrangement of the lens elements in an f lens of a fifth embodiment in accordance with the present invention, Figure 5B is a graph showing the lateral color aberration of the f lens shown in Figure 5A for three wavelengths W1, W2 and W3, Figure 5C is a graph showing the astigmatic field curves (curvature of field) of the f lens shown in Figure 5A for the three wavelengths W1, W2 and W3, Figure 5D is a graph showing the linearity (f characteristic) of the f lens shown in Figure 5A for the three wavelengths W1, W2 and W3, Figure 6A is a view showing the arrangement of the lens elements in an f lens of a sixth embodiment in accordance with the present invention, Figure 6B is a graph showing the lateral color aberration of the f lens shown in Figure 6A for three wavelengths W1, W2 and W3, Figure 6C is a graph showing the astigmatic field curves (curvature of field) of the f lens shown in Figure 6A for the three wavelengths W1, W2 and W3, Figure 6D is a graph showing the linearity (f characteristic) of the f lens shown in Figure 6A for the three wavelengths W1, W2 and W3, Figure 7A is a view showing the arrangement of the lens elements in an f lens of a seventh embodiment in accordance with the present invention, Figure 7B is a graph showing the lateral color aberration of the f lens shown in Figure 7A for three wavelengths W1, W2 and W3, Figure 7C is a graph showing the astigmatic field curves (curvature of field) of the f lens shown in Figure 7A for the three wavelengths W1, W2 and W3, Figure 7D is a graph showing the linearity (f characteristic) of the f lens shown in Figure 7A for the three wavelengths W1, W2 and W3, Figure 7A is a view showing the arrangement of the lens elements in an f lens of an eighth embodiment in accordance with the present invention, Figure 8B is a graph showing the lateral color aberration of the f lens shown in Figure 8A for three wavelengths W1, W2 and W3, Figure 8C is a graph showing the astigmatic field curves (curvature of field) of the f lens shown in Figure 8A for the three wavelengths W1, W2 and W3, Figure 8D is a graph showing the linearity (f characteristic) of the f lens shown in Figure 8A for the three wavelengths W1, W2 and W3, Figure 9A is a view showing the arrangement of the lens elements in an f lens of a ninth embodiment in accordance with the present invention, Figure 9B is a graph showing the lateral color aberration of the f lens shown in Figure 9A for three wavelengths W1, W2 and W3, Figure 9C is a graph showing the astigmatic field curves (curvature of field) of the f lens shown in Figure 9A for the three wavelengths W1, W2 and W3, Figure 9D is a graph showing the linearity (f characteristic) of the f lens shown in Figure 9A for the three wavelengths W1, W2 and W3, Figure 10A is a view showing the arrangement of the lens elements in an f lens of a tenth embodiment in accordance with the present invention, Figure 10B is a graph showing the lateral color aberration of the f lens shown in Figure 10A for three wavelengths W1, W2 and W3, Figure 10C is a graph showing the astigmatic field curves (curvature of field) of the f lens shown in Figure 10A for the three wavelengths W1, W2 and W3, Figure 10D is a graph showing the linearity (f characteristic) of the f lens shown in Figure 10A for the three wavelengths W1, W2 and W3, Figure 11A is a view showing the arrangement of the lens elements in an f lens of a eleventh embodiment in accordance with the present invention, Figure 11B is a graph showing the lateral color aberration of the f lens shown in Figure 11A for three wavelengths W1, W2 and W3, Figure 11C is a graph showing the astigmatic field curves (curvature of field) of the f lens shown in Figure 11A for the three wavelengths W1, W2 and W3, and Figure 11D is a graph showing the linearity (f characteristic) of the f lens shown in Figure 11A for the three wavelengths W1, W2 and W3. DESCRIPTION OF THE PREFERRED EMBODIMENTS f lenses of eleven embodiments in accordance with the present invention will be described with reference to Figures 1 (1A to 1D) to 11 (11A to 11D) and tables 1 to 11, hereinbelow. Figures 1A to 11A respectively show the arrangements of the lens elements of the f lenses of first to eleventh embodiments, and Figures 1B, 1C and 1D to 11B, 11C and 11D respectively show the lateral color aberration, the astigmatic field curves (curvature of field) and the linearity (f characteristic) of the f lenses of the first to eleventh embodiments when three laser beams having different wavelengths W1, W2 and W3 used in a scanning optical system enter the respective f lenses. The values of the wavelengths W1, W2 and W3 are shown on the top of the tables corresponding to the f lenses. Each of the f lenses in accordance with the present invention is for scanning light emanating from a deflecting point and comprises a first lens L1" having a positive refracting power and second lens L2" having a negative refracting power, the first and second lenses L1" and L2" being cemented together with the first lens L1" positioned on the entrance pupil side (deflecting point side). The f lens satisfies the following formulae (1) to (3), n d1 <n d2 0.4 ≦ ν d2 /ν d1 ≦ 0.8 1.5≦ 1 ≦4.7 wherein n d1 and n d2 respectively represent the refractive indexes for the sodium d-line of the first and second lenses L1" and L2", ν d1 and ν d2 respectively represent the Abbe's numbers for the sodium d-line of the first and second lenses L1" and L2", and  1 represents the power of the first lens L1" standardized on the basis of the power of the whole system. The f lens is used in a position where the distance do between the deflecting point and the entrance pupil side surface of the first lens L1" standardized on the basis of the focal length of the whole system is in the range of 0.1 to 0.4 inclusive (0.1≦d 0 ≦0.4;either of these values being standardized on the basis of the focal length of the whole system). In the first embodiment shown in Figure 1A, the factors respectively limited by the formulae (2) and (3) are set close to the lower limits of the ranges respectively defined by the formulae (2) and (3) and the distance do is set close to the upper limit. The radii of curvature R of the refracting surfaces, the axial surface separations d, and the refractive indexes nd and the Abbe's numbers ν d of the lenses for the sodium d-line in the f lens of this embodiment are shown in table 1. wavelength W1;680nm, W2;532nm, W3;473nm, angle of view 55.7° i Ri di n d ν d OBJ - infinity 0 infinity 0.30415 1 3.22923 0.10930 n d1 1.49700 ν d1 81.6 2 -0.27449 0.02376 n d2 1.72342 ν d2 38.0 3 -0.43441 0.99803 surface scanned infinity - n d1 = 1.497 , n d2 = 1.723 ν d1 /ν d2 = 0.47  1 = 1.95 d 0 =0.30415 lateral color aberration 0.138x10 -3 curvature of field 0.011 f characteristic 0.43% Figures 1B to 1D respectively show the lateral color aberration, the astigmatic field curves in the scanning direction and the linearity of the f lens of the first embodiment when laser beams having wavelengths of 680nm (W1), 532nm (W2) and 473nm (W3) enter the f lens. As can be understood from Figures 1B to 1D, in the f lens of this embodiment, the lateral color aberration is well corrected for the respective wavelengths in spite of a very simple structure consisting of only two lens elements in one lens group. In the second embodiment shown in Figure 2A, the ratio of the Abbe's number of the first lens to that of the second lend is set close to the lower limit of the range defined by the formula (2). The radii of curvature R of the refracting surfaces, the axial surface separations d, and the refractive indexes n d and the Abbe's numbers ν d of the lenses for the sodium d-line in the f lens of this embodiment are shown in table 2. wavelength W1;680nm, W2;532nm, W3;473nm, angle of view 55.7° i Ri di n d ν d OBJ - infinity 0 infinity 0.26657 1 2.79072 0.09520 n d1 1.48749 ν d1 70.4 2 -0.26207 0.02380 n d2 1.80610 ν d2 33.3 3 -0.39849 1.00254 surface scanned infinity - n d1 =1.487 , n d2 = 1.806 ν d1 /νd 2 = 0.47  1 = 2.02 d 0 = 0.26657 lateral color aberration 0.143x10 -3 curvature of field 0.011 f characteristic 0.77% Figures 2B to 2D respectively show the lateral color aberration, the astigmatic field curves in the scanning direction and the linearity of the f lens of the second embodiment when laser beams having wavelengths of 680nm (W1), 532nm (W2) and 473nm (W3) enter the f lens. As can be understood from Figures 2B to 2D, in the f lens of this embodiment, the lateral color aberration is well corrected for the respective wavelengths in spite of a very simple structure consisting of only two lens elements in one lens group. In the third embodiment shown in Figure 3A, the distance d 0 is set close to the lower limit. The radii of curvature R of the refracting surfaces, the axial surface separations d, and the refractive indexes nd and the Abbe's numbers ν d of the lenses for the sodium d-line in the f lens of this embodiment are shown in table 3. wavelength W1;680nm, W2;532nm, W3;473nm, angle of view 55.7° i Ri di n d ν d OBJ - infinity 0 infinity 0.14865 1 1.09840 0.06713 n d1 1.51680 ν d1 64.2 2 -0.14539 0.01918 n d2 1.67003 ν d2 47.2 3 -0.42289 0.98566 surface scanned infinity - n d1 = 1.517 , n d2 = 1.670 ν d1 /ν d2 = 0.74  1 = 3.97 d 0 = 0.14865 lateral color aberration 0.115x10 -3 curvature of field 0.027 f characteristic 2.90% Figures 3B to 3D respectively show the lateral color aberration, the astigmatic field curves in the scanning direction and the linearity of the f lens of the third embodiment when laser beams having wavelengths of 680nm (W1), 532nm (W2) and 473nm (W3) enter the f lens. As can be understood from Figures 3B to 3D, in the f lens of this embodiment, the lateral color aberration is well corrected for the respective wavelengths in spite of a very simple structure consisting of only two lens elements in one lens group. In the fourth embodiment shown in Figure 4A, the factors respectively limited by the formulae (2) and (3) are set close to the upper limits of the ranges respectively defined by the formulae (2) and (3). The radii of curvature R of the refracting surfaces, the axial surface separations d, and the refractive indexes n d and the Abbe's numbers ν d of the lenses for the sodium d-line in the f lens of this embodiment are shown in table 4. wavelength W1;680nm, W2;532nm, W3;473nm, angle of view 55.7° i Ri di n d ν d OBJ - infinity 0 infinity 0.15435 1 1.33208 0.05788 n d1 1.56883 ν d1 56.0 2 -0.14870 0.01929 n d2 1.72000 ν d2 42.0 3 -0.45323 0.99074 surface scanned infinity - n d1 = 1.569 , n d2 = 1.720 ν d1 /ν d2 = 0.75  1 = 4.21 d 0 = 0.15435 lateral color aberration 0.106x10 -3 curvature of field 0.027 f characteristic 3.00% Figures 4B to 4D respectively show the lateral color aberration, the astigmatic field curves in the scanning direction and the linearity of the f lens of the fourth embodiment when laser beams having wavelengths of 680nm (W1), 532nm (W2) and 473nm (W3) enter the f lens. As can be understood from Figures 4B to 4D, in the f lens of this embodiment, the lateral color aberration is well corrected for the respective wavelengths in spite of a very simple structure consisting of only two lens elements in one lens group. In the fifth embodiment shown in Figure 5A, the Abbe's number ν d1 of the first lens L1" is smaller than that in the other embodiments. The radii of curvature R of the refracting surfaces, the axial surface separations d, and the refractive indexes n d and the Abbe's numbers ν d of the lenses for the sodium d-line in the f lens of this embodiment are shown in table 5. wavelength W1;680nm, W2;532nm, W3;473nm, angle of view 55.7° Ri di n d ν d OBJ - infinity 0 infinity 0.16754 1 1.62437 0.06702 n d1 1.59270 ν d1 35.5 2 -0.17459 0.01436 n d2 1.80518 ν d2 25.5 3 -0.43526 0.99134 surface scanned infinity - n d1 = 1.593 , n d2 = 1.805 ν d1 /ν d2 = 0.72  1 = 3.74 d 0 = 0.16754 lateral color aberration 0.143x10 -3 curvature of field 0.022 f characteristic 2.41% Figures 5B to 5D respectively show the lateral color aberration, the astigmatic field curves in the scanning direction and the linearity of the f lens of the fifth embodiment when laser beams having wavelengths of 680nm (W1), 532nm (W2) and 473nm (W3) enter the f lens. As can be understood from Figures 5B to 5D, in the f lens of this embodiment, the lateral color aberration is well corrected for the respective wavelengths in spite of such a small Abbe's number of the first lens L1" as shown in table 29 and in spite of a very simple structure consisting of only two lens elements in one lens group. In the sixth embodiment shown in Figure 6A, the refractive index n d1 of the first lens L1" is higher than that in the other embodiments. The radii of curvature R of the refracting surfaces, the axial surface separations d, and the refractive indexes nd and the Abbe's numbers ν d of the lenses for the sodium d-line in the f lens of this embodiment are shown in table 6. wavelength W1;680nm, W2;532nm, W3;473nm, angle of view 55.7° Ri di n d ν d OBJ - infinity 0 infinity 0.20070 1 3.17313 0.07168 n d1 1.72000 ν d1 50.3 2 -0.19268 0.01911 n d2 1.83400 ν d2 37.3 3 -0.61013 0.99436 surface scanned infinity - n d1 = 1.720 , n d2 = 1.834 νd 1 /ν d2 = 0.74  1 = 3.95 d 0 = 0.20070 lateral color aberration 0.143x10 -3 curvature of field 0.018 f characteristic 2.06% Figures 6B to 6D respectively show the lateral color aberration, the astigmatic field curves in the scanning direction and the linearity of the f lens of the sixth embodiment when laser beams having wavelengths of 680nm (W1), 532nm (W2) and 473nm (W3) enter the f lens. As can be understood from Figures 6B to 6D, in the f lens of this embodiment, the lateral color aberration is well corrected for the respective wavelengths in spite of such a high refractive index of the first lens L1" as shown in table 30 and in spite of a very simple structure consisting of only two lens elements in one lens group. In the seventh embodiment shown in Figure 7A, the factors respectively limited by the formulae (2) and (3) are set substantially at the middle of the ranges respectively defined by the formulae (2) and (3). The radii of curvature R of the refracting surfaces, the axial surface separations d, and the refractive indexes nd and the Abbe's numbers ν d of the lenses for the sodium d-line in the f lens of this embodiment are shown in table 7. wavelength W1;810nm, W2;750nm, W3;680nm, angle of view 62.5° i Ri di n d ν d OBJ - infinity 0 infinity 0.19948 1 1.90834 0.08976 n d1 1.51680 ν d1 64.2 2 -0.20983 0.01995 n d2 1.71852 ν d2 33.5 3 -0.42608 0.99160 surface scanned infinity - n d1 = 1.517 , n d2 = 1.719 ν d1 /ν d2 = 0.52  1 = 2.67 d 0 = 0.19948 lateral color aberration 0.071x10 -3 curvature of field 0.024 f characteristic 1.49% Figures 7B to 7D respectively show the lateral color aberration, the astigmatic field curves in the scanning direction and the linearity of the f lens of the seventh embodiment when laser beams having wavelengths of 810nm (W1), 750nm (W2) and 680nm (W3) which are different from those of the laser beams used in the first to sixth embodiments enter the f lens. As can be understood from Figures 7B to 7D, in the f lens of this embodiment, the lateral color aberration is well corrected irrespective of wavelength in spite of a very simple structure consisting of only two lens elements in one lens group. In the eighth embodiment shown in Figure 8A, the factors respectively limited by the formulae (2) and (3) are set substantially at the middle of the ranges respectively defined by the formulae (2) and (3) as in the seventh embodiment. The radii of curvature R of the refracting surfaces, the axial surface separations d, and the refractive indexes n d and the Abbe's numbers ν d of the lenses for the sodium d-line in the f lens of this embodiment are shown in table. wavelength W1;870nm, W2;810nm, W3;750nm, angle of view 62.5° Ri di n d ν d OBJ - infinity 0 infinity 0.19905 1 1.64325 0.08957 n d1 1.51742 ν d1 52.2 2 -0.20875 0.01991 n d2 1.72825 ν d2 28.3 3 -0.43041 0.98895 surface scanned infinity - n d1 = 1.517 , n d2 = 1.728 ν d1 /ν d2 = 0.54  1 = 2.71 d 0 = 0.19905 lateral color aberration 0.064x10 -3 curvature of field 0.024 f characteristic 1.05% Figures 8B to 8D respectively show the lateral color aberration, the astigmatic field curves in the scanning direction and the linearity of the f lens of the eighth embodiment when laser beams having wavelengths of 870nm (W1), 810nm (W2) and 750nm (W3) which are different from those of the laser beams used in the first to seventh embodiments enter the f lens. As can be understood from Figures 8B to 8D, in the f lens of this embodiment, the lateral color aberration is well corrected irrespective of wavelength in spite of a very simple structure consisting of only two lens elements in one lens group. In the ninth embodiment shown in Figure 9A, the factors respectively limited by the formulae (2) and (3) are set substantially at the middle of the ranges respectively defined by the formulae (2) and (3) as in the seventh and eighth embodiments. The radii of curvature R of the refracting surfaces, the axial surface separations d, and the refractive indexes nd and the Abbe's numbers ν d of the lenses for the sodium d-line in the f lens of this embodiment are shown in table 9. wavelength W1;890nm, W2;830nm, W3;780nm, angle of view 62.5° Ri di n d ν d OBJ - infinity 0 infinity 0.19915 1 1.74894 0.08962 n d1 1.51742 ν d1 52.2 2 -0.21778 0.01991 n d2 1.80518 v d2 25.5 3 -0.40058 0.99321 surface scanned infinity - n d1 = 1.517 , n d2 = 1.805 ν d1 /ν d2 = 0.49  1 = 2.59 d 0 = 0.19915 lateral color aberration 0.028x10 -3 curvature of field 0.022 f characteristic 1.13% Figures 9B to 9D respectively show the lateral color aberration, the astigmatic field curves in the scanning direction and the linearity of the f lens of the ninth embodiment when laser beams having wavelengths of 890nm (W1), 830nm (W2) and 780nm (W3) which are different from those of the laser beams used in the first to eighth embodiments enter the f lens. As can be understood from Figures 9B to 9D, in the f lens of this embodiment, the lateral color aberration is well corrected irrespective of wavelength in spite of a very simple structure consisting of only two lens elements in one lens group. As can be understood from the description above, in the f lens in accordance with the present invention, the color aberration can be corrected with a high accuracy over a wide wavelength range, and accordingly, the error in superimposing the beam spots can be reduced in the scanning optical system or the like using a plurality of laser beams having different wavelengths. Further since being very simple in structure, the f lens in accordance with the third aspect of the present invention can be manufactured at low cost, and at the same time, the scanning optical system can be small in size, assembly of the f lens is facilitated and the error in assembly can be reduced. The f lens in accordance with the present invention need not be limited to those described above but may be variously modified so long as the formulae (1) to (3) are satisfied. The f lenses of tenth and eleventh embodiments shown in Figures 10A and 10A comprise an aspheric lens represented by the formula (13). In the tenth embodiment shown in Figure 10A, the second surface of the second lens L2" (the exit surface) is an aspheric surface as shown in table 10. Further, the factors respectively limited by the formulae (2) and (3) are set substantially at the middle of the ranges respectively defined by the formulae (2) and (3). The radii of curvature R of the refracting surfaces, the axial surface separations d, and the refractive indexes n d and the Abbe's numbers ν d of the lenses for the sodium d-line in the f lens of this embodiment are shown in table 10. In table 10, the value designated by represents the radius of curvature on the optical axis (at the vertex of the aspheric surface) and means that the aspheric surface has a shape defined by the following formula (4). (the same in table 11). x=ch 2 /[1+{1-(1+k)c 2 h 2 } 1/2 ]+a 1 h 4 +a 2 h 6 +a 3 h 8 +a 4 h 10 wherein x represents the length of a perpendicular line between a point on an aspheric plane at a height of h above the optical axis and a plane tangent to the aspheric plane (a plane perpendicular to the optical axis) (as standardized on the basis of the focal length of the whole system), h represents the height above the optical axis (as standardized on the basis of the focal length of the whole system), c represents the curvature at the vertex of the aspheric plane (the reciprocal of the radius of curvature = 1/R), k represents a conic constant, and a 1 to a 4 respectively represents four-dimensional, six-dimensional, eight-dimensional and ten-dimensional aspheric coefficients. Figures 10B to 10D respectively show the lateral color aberration, the astigmatic field curves in the scanning direction and the linearity of the f lens of the tenth embodiment when laser beams having wavelengths of 680nm (W1), 532nm (W2) and 473nm (W3) enter the f lens. As can be understood from Figures 10B to 10D, in the f lens of this embodiment, the lateral color aberration is well corrected for the respective wavelengths irrespective of a very simple structure consisting of only two lens elements in one lens group. In the eleventh embodiment shown in Figure 11A, the first surface of the first lens L1" (the entrance surface) is an aspheric surface as shown in table 11. Further, the factors respectively limited by the formulae (2) and (3) are set substantially at the middle of the ranges respectively defined by the formulae (2) and (3). The radii of curvature R of the refracting surfaces, the axial surface separations d, and the refractive indexes nd and the Abbe's numbers ν d of the lenses for the sodium d-line in the f lens of this embodiment are shown in table 11. Figures 11B to 11D respectively show the lateral color aberration, the astigmatic field curves in the scanning direction and the linearity of the f lens of the eleventh embodiment when laser beams having wavelengths of 680nm (W1), 532nm (W2) and 473nm (W3) enter the f lens. As can be understood from Figures 11B to 11D, in the f lens of this embodiment, the lateral color aberration is well corrected for the respective wavelengths irrespective of a very simple structure consisting of only two lens elements in one lens group.

Claims: A scanning optical system including a deflecting surface and a f lens for receiving scanning light emanating from said deflecting surface, said f lens comprising a first lens (L1") having a positive refracting power and a second lens (L2") having a negative refracting power, with the first lens positioned on the entrance pupil side, wherein the first and second lenses are cemented together and the following formulae (1) to (3) are satisfied n d1 < n d2 0.4 ≤ ν d2 /ν d1 ≤ 0.8 1.5 ≤  1 ≤ 4.7 wherein n d1 and n d2 respectively represent the refractive indices for the sodium d-line of the first and second lenses, ν d1 and ν d2 respectively represent the Abbe's numbers for the sodium d-line of the first and second lenses, and  1 represents the power of the first lens standardized on the basis of the power of the whole system, said f lens being used in a position where the distance between the deflecting point and the entrance pupil side surface of the first lens standardized on the basis of the focal length of the whole system is in the range of 0.1 to 0.4 inclusive.

Inventors: NOGUCHI MASARU, SHIMADA KATSUMI, NOGUCHI, MASARU, SHIMADA, KATSUMI, Noguchi, Masaru, c/o Fuji Photo Film Co., Ltd., Shimada, Katsumi, c/o Fuji Photo Film Co., Ltd.
Applicants: FUJI PHOTO FILM CO LTD, FUJI PHOTO FILM CO., LTD.
Application year: 1994
Main classification: G02B13
IPC codes: G02B13